Second order Runge-kutta methods for Itô stochastic differential equations

Andreas Rößler*

*Corresponding author for this work
32 Citations (Scopus)


A new class of stochastic Runge-Kutta methods for the weak approximation of the solution of Itô stochastic differential equation systems with a multidimensional Wiener process is introduced. As the main innovation, the number of stages of the methods does not depend on the dimension of the driving Wiener process, and the number of necessary random variables which have to be simulated is reduced considerably. Compared to well-known schemes, this reduces the computational efiort significantly. Order conditions for the stochastic Runge-Kutta methods assuring weak convergence with order two are calculated by applying the colored rooted tree analysis due to the author. Further, some coeficients for explicit second order stochastic Runge-Kutta schemes are presented.

Original languageEnglish
JournalSIAM Journal on Numerical Analysis
Issue number3
Pages (from-to)1713-1738
Number of pages26
Publication statusPublished - 01.06.2009


Dive into the research topics of 'Second order Runge-kutta methods for Itô stochastic differential equations'. Together they form a unique fingerprint.

Cite this